Cosmological curvature acceleration

Observed accelerated behavior of the Hubble flow, usually related to the existence of a mysterious unknown fluid dubbed dark energy, can be framed in natural extensions of General Relativity that work at infrared scales. This approach gives rise to a geometric view of the phenomenon that does not require any new particle to be addressed. In this review paper, without claiming for completeness, we will give the main ingredients of such an approach considering models like f(R) gravity, with R the Ricci curvature scalar, and, in general, higher-order theories of gravity including other curvature invariants. In this context, we will review also Teleparallel Equivalent General Relativity and its extensions like f(T) gravity, where T is the torsion scalar. We will show that the curvature picture and the torsion picture can be related each other giving an equivalent paradigm where the observed cosmological acceleration can be addressed by extending the gravitational sector.